Band extending apparatus and method

ABSTRACT

A band extending apparatus ( 1 ) is provided with: first generating device ( 111, 112 ) for generating a baseband signal (X B (n)) by up-sampling an input signal (X(n)) and then transmitting it through a low-pass filter; a second generating device ( 21 ) for generating a high-frequency signal (X H (n)), by extracting a signal component on a higher-frequency side of a signal which is obtained by squaring a band limited signal (X b (n)) which is a signal component with a predetermined band of the baseband signal; and a third generating device ( 141 ) for generating an output signal (X E (n)) by adding the high-frequency signal to the baseband signal.

TECHNICAL FIELD

The present invention relates to a band extending apparatus (bandspreading) for extending the band of an input signal such as an audiosignal.

BACKGROUND ART

As a technology of extending the band of a digital audio signal, such atechnology is known that a predetermined nonlinear process is performedon the digital audio signal to be inputted, to thereby generate ahigher-frequency signal component than the digital audio signal to beinputted (refer to a patent document 1 and a non patent document 1). Forexample, in the technology disclosed in the patent document 1, thehigher-frequency signal component than the digital audio signal to beinputted is generated by performing full-wave rectification, which is totake an absolute value of the digital audio signal to be inputted.

Patent document 1: Japanese Patent Application Publication NO.2003-317395Non Patent document 1: Ronald M. Aarts and Erik Larsen and DanielSchobben, “IMPROVING PERCEIVED BASS AND RECONSTRUCTION OF HIGHFREQUENCIES FOR BAND LIMITED SIGNALS”, Proc. 1st IEEE Benelux Workshopon Model based Processing and Coding of Audio (MPCA-2002), Belgium, Nov.15, 2002, pp 59-71

DISCLOSURE OF INVENTION Subject to be Solved by the Invention

However, if the predetermined nonlinear process is performed on thedigital audio signal to be inputted, as described above, not only adouble sound component and a sum sound (summational sound) component,which are originally desired to be generated, but also a direct currentcomponent and a difference sound component are generated simultaneously.Moreover, a signal component which has no harmonic relationship with thedigital audio signal to be inputted is also generated simultaneously. Ifit is attempted to extract the double sound component and the sum soundcomponent, which are originally desired to be generated, from the signalincluding these unnecessary signal components, a high pass filter havinga large attenuation and a sharp shut off feature is required. However,the high pass filter having such a feature likely has a large circuitscale (in other words, a large amount of operation or calculation).

It is therefore an object of the present invention to provide a bandextending apparatus and method which enable the band of the input signalto be extended more appropriately, for example.

Means for Solving the Subject

The above object of the present invention can be achieved by a bandextending apparatus according to claim 1, provided with: a firstgenerating device for generating a baseband signal by up-sampling aninput signal and then transmitting it through a low-pass filter; asecond generating device for generating a high-frequency signal, whichis a signal component corresponding to the input signal and which is asignal component on a higher-frequency side than the input signal, byextracting a signal component on a higher-frequency side of a signalwhich is obtained by squaring a band limited signal, the band limitedsignal is a signal component with a predetermined band of the basebandsignal; and a third generating device for generating an output signal byadding the high-frequency signal to the baseband signal.

The above object of the present invention can be also achieved by a bandextending method according to claim 10, provided with: a firstgenerating process of generating a baseband signal by up-sampling aninput signal and then transmitting it through a low-pass filter; asecond generating process of generating a high-frequency signal, whichis a signal component corresponding to the input signal and which is asignal component on a higher-frequency side than the input signal, onthe basis of a signal component on a higher-frequency side of a signalwhich is obtained by squaring a band limited signal, the band limitedsignal is a signal component with a predetermined band of the basebandsignal; and a third generating process of generating an output signal byadding the high-frequency signal to the baseband signal.

The effects and other advantages of the present invention will becomemore apparent from the embodiments explained below.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram conceptually showing the basic structure of afirst example of the band extending apparatus of the present invention.

FIG. 2 are spectrum views conceptually showing the spectrum of each ofan input signal, a baseband signal, and a band limited signal, relatedto the operation of the band extending apparatus in the first example.

FIG. 3 are spectrum views conceptually showing the spectrum of each of ahigh-frequency signal and a band extension signal, related to theoperation of the band extending apparatus in the first example.

FIG. 4 is a block diagram conceptually showing a more specific structureof a gain calculation circuit.

FIG. 5 is a spectrum view showing the baseband signal.

FIG. 6 is a spectrum view showing a band extension signal generated bythe baseband signal shown in FIG. 5.

FIG. 7 is a spectrum view showing the band limited signal.

FIG. 8 is a spectrum view showing a signal obtained by squaring the bandlimited signal shown in FIG. 7.

FIG. 9 is a spectrum view showing a signal after the band limited signalshown in FIG. 7 is full-wave rectified by the operation of a bandextending apparatus in a comparison example.

FIG. 10 is a block diagram conceptually showing the basic structure of asecond example of the band extending apparatus of the present invention.

FIG. 11 is a block diagram conceptually showing the basic structure of athird example of the band extending apparatus of the present invention.

FIG. 12 are spectrum views conceptually showing the spectrum of each ofthe input signal, the baseband signal, and the signal componentextracted by the band extraction circuit, related to the operation ofthe band extending apparatus in the third example.

FIG. 13 is an explanatory diagram conceptually showing a blockmultiplied by a Hanning window.

FIG. 14 is a spectrum view conceptually showing an operation ofdetermining upper-end frequency.

FIG. 15 are spectrum views conceptually showing the spectrum of each ofthe high-frequency signal and the band extension signal, related to theoperation of the band extending apparatus in the third example.

FIG. 16 is a spectrum view showing a signal obtained by squaring theband limited signal shown in FIG. 7.

FIG. 17 is a block diagram conceptually showing the basic structure of afourth example of the band extending apparatus of the present invention.

FIG. 18 is a block diagram conceptually showing the basic structure of afifth example of the band extending apparatus of the present invention.

FIG. 19 are block diagrams conceptually showing the structure when theband extending apparatus is applied to various products.

DESCRIPTION OF REFERENCE CODES

-   1, 2, 3, 4, 5 band extending apparatus-   111, 112 up-sampling circuit-   121, 122 LPF-   131, 162 delay circuit-   141, 142 adder circuit-   151 BPF-   173 blocking circuit-   183 windowing circuit-   21, 23 high-frequency signal generation circuit-   211 square circuit-   212 HPF-   214 gain calculation circuit-   215 gain adjustment circuit-   231 square-root windowing circuit-   232, 234 FFT circuit-   233 band extraction circuit-   235 upper-end frequency determination circuit-   216 IFFT circuit

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, as the best mode for carrying out the invention, anexplanation will be given on embodiments of the band extending apparatusand method of the present invention.

(Embodiment of Band Extending Apparatus)

An embodiment of the band extending apparatus of the present inventionis a band extending apparatus provided with: a first generating devicefor generating a baseband signal by up-sampling an input signal and thentransmitting it through a low-pass filter; a second generating devicefor generating a high-frequency signal, which is a signal componentcorresponding to the input signal and which is a signal component on ahigher-frequency side than the input signal, by extracting a signalcomponent on a higher-frequency side of a signal which is obtained bysquaring a band limited signal, the band limited signal is a signalcomponent with a predetermined band of the baseband signal; and a thirdgenerating device for generating an output signal by adding thehigh-frequency signal to the baseband signal.

According to the embodiment of the band extending apparatus of thepresent invention, the sampling frequency of the input signal isup-sampled by the operation of the first generating device and then theinput signal is transmitted through the low-pass filter. By this, thebaseband signal is generated from the input signal.

Then, by the operation of the second generating device, thehigh-frequency signal which has a harmonic relationship with the inputsignal and which has the frequency on the higher-frequency side than thefrequency of the input signal (more specifically, for example, a doublesound component, a sum sound component, or the like of the frequencycomponent of the input signal) is generated from the signal obtained bysquaring the band limited signal, which is the signal component with thepredetermined band of the baseband signal (more specifically, the signalcomponent with the band which becomes a base for generating thehigh-frequency signal). More specifically, the high-frequency signal isgenerated by extracting the high-frequency component of the signalobtained by squaring the band limited signal (more specifically, thesignal component on the higher-frequency side than the frequency of theinput signal) using a HPF (High Pass Filter) or the like.

Then, by the operation of the third generating device, the outputsignal, which is a signal obtained by extending the band of the inputsignal to the higher-frequency side, is generated by adding thegenerated high-frequency signal to the baseband signal.

As described above, according to the band extending apparatus in theembodiment, it is possible to extend the band of the input signal. Thatis, it is possible to preferably generate the high-frequency signalwhich has the harmonic relationship with the input signal and which hasthe frequency on the higher-frequency side than the frequency of theinput signal.

In one aspect of the embodiment of the band extending apparatus of thepresent invention, the second generating device generates thehigh-frequency signal by adjusting a gain of the high-frequency signalin accordance with an absolute value of the band limited signal.

According to this aspect, the amplitude level of the high-frequencysignal can be adjusted to the amplitude level of the original basebandsignal (or input signal). Specifically, as described above, since thehigh-frequency signal is generated by squaring the band limited signal,the amplitude level of the high-frequency signal is on the order of thesquare of the amplitude level of the original baseband signal (or inputsignal). Thus, by adjusting the gain of the high-frequency signal inaccordance with the absolute value of the band limited signal, it ispossible to adjust the amplitude level of the high-frequency signal tothe amplitude level of the original baseband signal (or input signal).

In another aspect of the embodiment of the band extending apparatus ofthe present invention, it is further provided with a delaying device foradding a delay corresponding to a time required for the generation ofthe high-frequency signal by the second generating device, to thebaseband signal, the third generating device adding the high-frequencysignal to the baseband signal to which the delay corresponding to thetime required for the generation of the high-frequency signal by thesecond generating device is added.

According to this aspect, since the delay of the time required for thegeneration of the high-frequency signal is added to the baseband signal,the high-frequency signal corresponding to the same time as the basebandsignal can be added to the baseband signal. That is, the high-frequencysignal generated in accordance with the baseband signal at a certaintime can be added to the baseband signal at the certain time. By this,it is possible to eliminate an influence by the delay of the timerequired for the generation of the high-frequency signal.

In another aspect of the embodiment of the band extending apparatus ofthe present invention, the predetermined band is a band ranged between ½of a upper-end frequency of the input signal and ½ of a samplingfrequency of the input signal before being up-sampled.

By virtue of such construction, it is possible to preferably generatethe high-frequency signal, using the band limited signal, which is asignal component with the band ranged between ½ of the upper-endfrequency of the input signal and ½ of the sampling frequency of theinput signal before being up-sampled.

In another aspect of the embodiment of the band extending apparatus ofthe present invention, the second generating device is further providedwith: a Fourier transforming device for generating a Fourier transformsignal by performing a Fourier transform process on the baseband signal;a determining device for determining a frequency at which a signal levelof the Fourier transform signal is suddenly dropped, as an upper-endfrequency; a changing device for changing a level of the Fouriertransform signal so as to maintain a level of a signal component with aband defined in accordance with the upper-end frequency, of the Fouriertransform signal, and to zero a level of a signal component other thanthe signal component with the band defined in accordance with theupper-end frequency, of the Fourier transform signal; and an inverseFourier transforming device for generating an inverse Fourier transformsignal by performing an inverse Fourier transform process on the Fouriertransform signal in which the level is changed by the changing device,and the second generating device generates the high-frequency signal,with using the inverse Fourier transform signal as the band limitedsignal.

According to this aspect, the Fourier transform process is performed onthe baseband signal, by the operation of the Fourier transformingdevice. As a result, the Fourier transform signal is generated. Then,the upper-end frequency, which is the frequency at which the signallevel of the Fourier transform signal is suddenly dropped, is determinedon the basis of the generated Fourier transform signal, by the operationof the determining device. Then, the level of the Fourier transformsignal is maintained by the operation of the changing device so as tomaintain the level of the signal component with the band defined inaccordance with upper-end frequency of the Fourier transform signal. Inthe same manner, the level of the Fourier transform signal is changed bythe operation of the changing device so as to zero the level of thesignal component other than the signal component with the band definedin accordance with the upper-end frequency, of the Fourier transformsignal. Then, the inverse Fourier transform process is performed on theFourier transform signal in which the level is changed by the changingdevice, by the operation of the inverse Fourier transforming device. Asa result, the inverse Fourier transform signal is generated.

The second generating device can generate the high-frequency signal, bytreating the inverse Fourier transform signal as the band limitedsignal.

As described above, even if the baseband signal is treated in thefrequency area in the Fourier transform process and the inverse Fouriertransform process, the high-frequency signal can be preferablygenerated.

In particular, the band of the inverse Fourier transform signal treatedas the band limited signal is defined in accordance with the upper-endfrequency, which is determined by the operation of the determiningdevice, as occasion demands. Therefore, without simply relying on theupper-end frequency of the baseband signal (in other words, the inputsignal) to be inputted, it is possible to generate the high-frequencysignal, appropriately in accordance with the baseband signal to beinputted (specifically, while maintaining the continuity with thebaseband signal to be inputted).

In an aspect of the band extending apparatus provided with the Fouriertransforming device as described above, the changing device may changethe level of the Fourier transform signal so as to maintain a level of asignal component with a band ranged between ½ of the upper-end frequencyand ½ of a sampling frequency of the input signal before beingup-sampled, of the Fourier transform signal, and to zero a level of asignal component other than the signal component with the band rangedbetween ½ of the upper-end frequency and ½ of the sampling frequency ofthe input signal before being up-sampled, of the Fourier transformsignal.

By virtue of such construction, it is possible to generate thehigh-frequency signal, appropriately in accordance with the basebandsignal to be inputted (specifically, while maintaining the continuitywith the baseband signal to be inputted).

In an aspect of the band extending apparatus provided with the Fouriertransforming device as described above, the band extending apparatus maybe further provided with: a dividing device for dividing the basebandsignal into a plurality of block in which one portion of each of theplurality of blocks overlaps adjacent blocks; and a first windowingdevice for performing a windowing process using a Hanning window, on thebaseband signal divided into the plurality of blocks, the secondgenerating device may be further provided with a second windowing devicefor performing a windowing process using a square root of a Hanningwindow, on the baseband signal divided into the plurality of blocks, theFourier transforming device may perform the Fourier transform process oneach of the baseband signal on which the windowing process using theHanning window is performed and the baseband signal on which thewindowing process using the square root of the Hanning window isperformed, the determining device may determine the frequency at whichthe signal level of the Fourier transform signal, generated byperforming the Fourier transform process on the baseband signal on whichthe windowing process using the Hanning window is performed, is suddenlydropped, as the upper-end frequency, and the changing device may changethe level of the Fourier transform signal so as to maintain a level of asignal component with a band defined in accordance with the upper-endfrequency, of the Fourier transform signal generated by performing theFourier transform process on the baseband signal on which the windowingprocess using the square root of the Hanning window is performed, and tozero a level of a signal component other than the signal component witha band defined in accordance with the upper-end frequency, of theFourier transform signal generated by performing the Fourier transformprocess on the baseband signal on which the windowing process using thesquare root of the Hanning window is performed.

By virtue of such construction, the baseband signal is divided into theplurality of blocks in which one portion of each block overlaps adjacentblocks, and the windowing process using the Hanning window is performed.Thus, in the case where the inverse Fourier transform process isperformed on the baseband signal with the Fourier transform processperformed (i.e. the Fourier transform signal), it is possible toregenerate the original baseband signal without distortion.

In an aspect of the band extending apparatus provided with the Fouriertransforming device as described above, the band extending apparatus maybe further provided with a dividing device for dividing the basebandsignal into a plurality of block in which one portion of each of theplurality of blocks overlaps adjacent blocks, the second generatingdevice may be further provided with a windowing device for performing awindowing process using a square root of a Hanning window, on thebaseband signal divided into the plurality of blocks, the Fouriertransforming device may perform the Fourier transform process on each ofthe baseband signal on which the windowing process using the square rootof the Hanning window is performed, the determining device may determinethe frequency at which the signal level of the Fourier transform signal,generated by performing the Fourier transform process on the basebandsignal on which the windowing process using the square root of theHanning window is performed, is suddenly dropped, as the upper-endfrequency, and the changing device may change the level of the Fouriertransform signal so as to maintain a level of a signal component with aband defined in accordance with the upper-end frequency, of the Fouriertransform signal generated by performing the Fourier transform processon the baseband signal on which the windowing process using the squareroot of the Hanning window is performed, and to zero a level of a signalcomponent other than the signal component with a band defined inaccordance with the upper-end frequency, of the Fourier transform signalgenerated by performing the Fourier transform process on the basebandsignal on which the windowing process using the square root of theHanning window is performed.

By virtue of such construction, the baseband signal is divided into theplurality of blocks in which one portion of each block overlaps adjacentblocks, and the windowing process using the Hanning window is performed.Thus, in the case where the inverse Fourier transform process isperformed on the baseband signal with the Fourier transform processperformed (i.e. the Fourier transform signal), it is possible toregenerate the original baseband signal without distortion.

In another aspect of the embodiment of the band extending apparatus ofthe present invention, the band extending apparatus is provided with aplurality of second generating devices, and one second generating deviceof the plurality of second generating devices generates a newhigh-frequency signal by extracting a signal component on ahigher-frequency side of a signal obtained by squaring thehigh-frequency signal, which is generated by at least one of the secondgenerating devices other than the one second generating device.

According to this aspect, the new high-frequency signal including thesignal component on the much higher-frequency side than thehigh-frequency signal can be generated by the operation of anothersecond generating device, on the basis of the high-frequency signalgenerated by the second generating device. That is, since the secondgenerating devices can be multistage-combined, it is possible to extendthe band of the input signal, more widely.

(Embodiment of Band Extending Method)

An embodiment of the band extending method of the present invention is aband extending method provided with: a first generating process ofgenerating a baseband signal by up-sampling an input signal and thentransmitting it through a low-pass filter; a second generating processof generating a high-frequency signal, which is a signal componentcorresponding to the input signal and which is a signal component on ahigher-frequency side than the input signal, on the basis of a signalcomponent on a higher-frequency side of a signal which is obtained bysquaring a band limited signal, the band limited signal is a signalcomponent with a predetermined band of the baseband signal; and a thirdgenerating process of generating an output signal by adding thehigh-frequency signal to the baseband signal.

According to the embodiment of the band extending method of the presentinvention, it is possible to receive the same effects as those of theembodiment of the band extending apparatus of the present inventiondescribed above.

Incidentally, in response to the various aspects in the embodiment ofthe band extending apparatus of the present invention described above,the embodiment of the band extending method of the present invention canalso employ various aspects.

The effects and other advantages of the embodiments will become moreapparent from the examples explained below.

As explained above, according to the embodiment of the band extendingapparatus of the present invention, it is provided with the firstgenerating device, the second generating device, and the thirdgenerating device. According to the embodiment of the band extendingmethod of the present invention, it is provided with the firstgenerating process, the second generating process, and the thirdgenerating process. Therefore, it is possible to extend the band of theinput signal, more appropriately.

EXAMPLES

Hereinafter, examples of the present invention will be explained on thebasis of the drawings.

(1) First Example

Firstly, with reference to FIG. 1 to FIG. 9, an explanation will begiven on a first example of the band extending apparatus of the presentinvention.

(1-1) Basic Structure

Firstly, with reference to FIG. 1, an explanation will be given on thebasic structure of the first example of the band extending apparatus ofthe present invention. FIG. 1 is a block diagram conceptually showingthe basic structure of the first example of the band extending apparatusof the present invention.

As shown in FIG. 1, a band extending apparatus 1 in the first example isprovided with: an up-sampling circuit 111; a LPF (Low Pass Filter) 121;a delay circuit 131; an adder 141; a BPF (Band Pass Filter) 151; and ahigh-frequency signal generation circuit 21.

The up-sampling circuit 111 up-samples sampling frequency f_(s) of aninput signal x(n), which is a digital signal, for example by a factor of2. The input signal x(n) whose sampling frequency if, is up-sampled onthe up-sampling circuit 111 is outputted to the LPF 121.

The LPF 121 transmits therethrough a signal component with a band of 0to π/2 (i.e. π/2), of the input signal x(n) whose sampling frequency f,is up-sampled. The signal component with the band of 0 to f_(s)/2 (i.e.π/2) corresponds to a baseband signal x_(B)(n), The baseband signalx_(B)(n) is outputted to each of the delay circuit 131 and the BPF 151.

Incidentally, the up-sampling circuit 111 and the LPF 121 constitute onespecific example of the “first generating device” of the presentinvention.

The delay circuit 131 constitutes one specific example of the “delayingdevice” of the present invention. The delay circuit 131 adds a delay A,which corresponds to the time required for signal processing on the BPF151 and the high-frequency signal generation circuit 21, to the basebandsignal x_(B)(n). The baseband signal x_(B)(n) to which the delay A isadded on the delay circuit 131 is outputted to the adder 141.

The adder 141 constitutes one specific example of the “third generatingdevice” of the present invention. The adder 141 adds the baseband signalx_(B)(n) outputted from the delay circuit 131 and a high-frequencysignal x_(H)(n) generated on the high-frequency signal generationcircuit 21, to thereby generate a band extension signal (in other words,output signal) x_(E)(n).

The BPF 151 extracts a band limited signal x_(b)(n), which is a signalcomponent with a band that becomes a basis for generating thehigh-frequency signal x_(H)(n), from the baseband signal x_(B)(n). Morespecifically, the BPF 151 extracts the band limited signal x_(b)(n),which is a signal component with a band between ½ of the upper-limitfrequency of the input signal x(n) and F_(s)/2, from the baseband signalx_(B)(n), The band limited signal x_(b)(n) extracted on the BPF 151 isoutputted to the high-frequency generation circuit 21.

The high-frequency signal generation circuit 21 constitutes one specificexample of the “second generating device” of the present invention. Thehigh-frequency signal generation circuit 21 generates the high-frequencysignal x_(H)(n), which is a signal component on the higher-frequencyside than the frequency of the signal components included in the inputsignal x(n). More specifically, the high-frequency signal generationcircuit 21 is provided with: a square circuit 211; a HPF (High PassFilter) 212; a gain calculation circuit 214; and a gain adjustmentcircuit 215.

The square circuit 211 squares the band limited signal x_(b)(n)outputted from the BPF 151. The squared band limited signal x_(b)(n) isoutputted to the HPF 212.

The HPF 212 extracts a signal component on the higher-frequency side ofthe squared band limited signal x_(b)(n). The extracted signal componenton the higher-frequency side corresponds to the high-frequency signalx_(H)(n). The high-frequency signal x_(H)(n) is outputted to the gainadjustment circuit 215.

The gain calculation circuit 214 calculates a gain G(n) of thehigh-frequency signal x_(H)(n), on the basis of the band limited signalx_(b)(n) outputted from the BPF 151.

The gain adjustment circuit 215 multiplies the high-frequency signalx_(H)(n) by the gain G(n) calculated on the gain calculation circuit214. By this, the gain of the high-frequency signal x_(H)(n) isadjusted. The high-frequency signal x_(H)(n) whose gain is adjusted onthe gain adjustment circuit 215 is outputted to the adder 141.

(1-2) Operation Principle

Next, with reference to FIG. 2 and FIG. 3, an explanation will be givenon the operation principle of the band extending apparatus 1 in thefirst example. FIG. 2 are spectrum views conceptually showing thespectrum of each of the input signal x(n), the baseband signal x_(B)(n),and the band limited signal x_(b)(n), related to the operation of theband extending apparatus 1 in the first example. FIG. 3 are spectrumviews conceptually showing the spectrum of each of the high-frequencysignal x_(H)(n) and the band extension signal x_(E)(n), related to theoperation of the band extending apparatus 1 in the first example.

As shown in FIG. 2( a), it is assumed that the input signal x(n) withthe sampling frequency f_(s) is inputted to the band extending apparatus1.

For the input signal x(n), the up-sampling circuit 111 up-samples thesampling frequency f_(s) by a factor of 2. Then, the LPF 121 extractsthe signal component with the band of 0 to f/2 (i.e. π/2), from theinput signal x(n) whose sampling frequency f, is up-sampled. As aresult, the baseband signal x_(B)(n) shown in FIG. 2( b) is extracted.

Then, the BPF 151 extracts the signal component with the band between ½of the upper-limit frequency of the input signal x(n) and f_(s)/2, fromthe extracted baseband signal x_(B)(n). As a result, the band limitedsignal x_(b)(n) shown in FIG. 2( c) is extracted.

Then, the square circuit 211 squares the band limited signal x_(b)(n)extracted on the BPF 151. That is, the square circuit 211 generatesx_(b) ²(n).

Then, the HPF 212 extracts a signal component on the higher-frequencyside of the squared band limited signal x_(b)(n) (i.e. x_(b) ²(n)).Specifically, the HPF 212 extracts the signal component on thehigher-frequency side than the frequency of the baseband signal x_(B)(n)(or the input signal x(n)).

Here, it is assumed that the band limited signal x_(b)(n) is denoted byx_(b)(n)=A sin(ω₁t)+B sin(ω₂t). In this case, the signal x_(b) ²(n)obtained by squaring the band limited signal x_(b)(n) is x_(b) ²(n) (Asin(ω₁t)+B sin(ω₂t))²=(A²+B²)/2−A² cos(2ω₁t)/2−B² cos(2ω₂t)/2+ABcos((ω₁−ω₂)t). That is, the squared band limited signal x_(b)(n)includes a double sound component (specifically, a component denoted byangular frequency of 2ω₁ and 2ω₂) of a frequency component of the bandlimited signal x_(b)(n) (specifically, a component denoted by angularfrequency of ω₁ and ω₂), and a sum sound component (specifically, acomponent denoted by angular frequency of ω₁+ω₂), as well as adifference sound component (specifically, a component denoted by angularfrequency of ω₁−ω₂) of a frequency component of the band limited signalx_(b)(n) and a direct current component. Thus, the high-frequency signalx_(H)(n) is generated by extracting the double sound component and thesum sound component (i.e. the signal components on the higher-frequencyside) from the squared band limited signal x_(b)(n).

In particular, this will be explained in details later using a graph(refer to FIG. 5 to FIG. 9), but the squared band limited signalx_(b)(n) does not include an original signal component. That is,although the squared band limited signal x_(b)(n) includes the doublesound component and the sum sound component as well as the differencesound component and the direct current component, there is no signalcomponent included between the double sound component/the sum soundcomponent and the difference sound component/the direct currentcomponent. Therefore, the shutoff feature of the HPF 212 can be mild,and the circuit scale of the filter can be relatively reduced. Forexample, the blocking range of the HPF 212 may be 0 to about π/4, andthe passing range may be about π/2 to π.

However, the amplitude level of the high-frequency signal x_(H)(n) is onthe square order of the amplitude level of the band Limited signalx_(b)(n), such as A², AB, and B². Thus, such a process is performed thatcorrects the amplitude level of the squared band limited signal x_(b)(n)generated on the square circuit 211, to the original amplitude levelorder. Specifically, firstly, before the band limited signal x_(b)(n) issquared on the square circuit 211, the band limited signal x_(b)(n) isdivided by the square root of the maximum amplitude of the band limitedsignal x_(b)(n) in advance. The square root of the maximum amplitude ofthe band limited signal x_(b)(n) is, for example, (2^(n)−1)^(1/2) if theband limited signal x_(b)(n) is expressed by n bits. Specifically, thesquare root of the maximum amplitude of the band limited signal x_(b)(n)is (2¹⁶−1)^(1/2)≈181 if the band limited signal x_(b)(n) is expressed by16 bits. The division operation is performed on the band limited signalx_(b)(n), which is the output of the BPF 151. Then, on the squarecircuit 211, the squared band limited signal x_(b) ²(n) is generated bysquaring the band limited signal x_(b)(n) divided by the square root ofthe maximum amplitude.

Moreover, by virtue of the operations of the gain calculation circuit214 and the gain adjustment circuit 215 or the like, a gain adjustmentprocess is performed, wherein the gain adjustment process is to correctthe amplitude level of the high-frequency signal x_(H)(n) generated onthe HPF 212 to the original amplitude level order.

Now, the gain adjustment process will be explained while a more specificexample of the gain calculation circuit 214 is explained. FIG. 4 is ablock diagram conceptually showing the more specific structure of thegain calculation circuit 214.

As shown in FIG. 4, the gain calculation circuit 214 is provided with:an absolute value extraction circuit 244; a smoothing circuit 245; and acalculation circuit 246.

As for the band limited signal x_(b)(n) outputted from the BPF 151, itsabsolute value |x_(b)(n)| is calculated by the operation of the absolutevalue extraction circuit 244.

Then, in order to inhibit an abrupt change in the absolute value|x_(b)(n)| of the band limited signal x_(b)(n), a smoothing process isperformed on the absolute value |x_(b)(n)| of the band limited signalx_(b)(n), by the operation of the smoothing circuit 245. Specifically,the smoothed absolute value |x_(b)(n)| of the band limited signalx_(b)(n) (hereinafter referred to as a “smoothed absolute value” asoccasion demands), s(n), is denoted by s(n)=(1−α)×s(n−1)+α×|x_(b)(n)|.Here, the “α” is a constant defined in a range between 0 and 1, in orderto adjust the degree of smoothing. That is, in accordance with an aspectof the change in the absolute value |x_(b)(n)| of the band limitedsignal x_(b)(n), a preferable value is determined as the constant α, asoccasion demands.

Then, the gain G(n) actually multiplied by the high-frequency signalx_(H)(n) outputted from the HPF 212 is calculated by the operation ofthe calculation circuit 246.

Specifically, the gain G(n) is denoted by AMAX/(s(n)+c) if the maximumvalue of the smoothed absolute value is AMAX. Here, “c” is a smallconstant to prevent such a disadvantage that the denominator becomes 0,and a preferable value is set as occasion demands. Moreover, the maximumvalue of the smoothed absolute value, AMAX, is for example(2^(n)−1)^(1/2) if the band limited signal x_(b)(n) is expressed by nbits. Specifically, the maximum value of the smoothed absolute value is(2¹⁶−1)^(1/2)≈181 if the band limited signal x_(b)(n) is expressed by 16bits.

However, if the maximum value of the gain G(n) is GMAX, which isintroduced from the viewpoint of preventing the gain G(n) from being toolarge for a small signal such as a noise, the gain G(n) is GMAX whenEMAX/(s(n)+c) is greater than GMAX.

The gain G(n) calculated in this manner is multiplied by thehigh-frequency signal x_(H)(n) generated on a multiplier 213, by theoperation of the gain adjustment circuit 215. The high-frequency signalx_(H)(n) multiplied by the gain G(n) is added to the baseband signalx_(B)(n) on the adder 141. As a result, as shown in FIG. 3( b), the bandextension signal x_(E)(n) is generated.

Incidentally, the delay A, which corresponds to the time required togenerate the high-frequency signal x_(H)(n) by the operations of the BPF151 and the high-frequency signal generation circuit 21, is added to thebaseband signal x_(B)(n) added on the adder 141, by the operation of thedelay circuit 131. In other words, the delay circuit 131 adjusts thetime between the baseband signal x_(B)(n) extracted on the LPF 121 andthe high-frequency signal x_(H)(n) generated on the high-frequencysignal generation circuit 21. Moreover, in other words, the delaycircuit 131 adds the delay A to the baseband signal x_(B)(n) such thatthe baseband signal x_(B)(n) corresponding to a certain time and thehigh-frequency signal x_(H)(n) generated from the baseband signalx_(B)(n) corresponding to the certain time are added on the adder 141.

Now, with reference to FIG. 5 to FIG. 9, an explanation will be given onthe band limited signal x_(b)(n), the band extension signal x_(E)(n),and the high-frequency signal x_(H)(n), generated by the band extendingapparatus 1 in the first example. FIG. 5 is a spectrum view showing thebaseband signal x_(B)(n). FIG. 6 is a spectrum view showing the bandextension signal x_(E)(n) generated from the baseband signal x_(B)(n)shown in FIG. 5. FIG. 7 is a spectrum view showing the band limitedsignal x_(b)(n). FIG. 8 is a spectrum view showing a signal x_(b) ²(n)obtained by squaring the band limited signal x_(b)(n) shown in FIG. 7.FIG. 9 is a spectrum view showing a signal after the band limited signalx_(b)(n) shown in FIG. 7 is full-wave rectified by the operation of aband extending apparatus in a comparison example.

FIG. 5 shows a signal obtained by extracting e.g. a signal componentwith about 10000 Hz or less, from a signal with a sampling frequency of44.1 kHz. This corresponds to the baseband signal x_(B)(n), obtained byup-sampling the input signal x(n) having a sampling frequency of 22.05kHz by a factor of 2 and then transmitting it through the LPF.

If a band extension process is performed on the baseband signal x_(B)(n)shown in FIG. 5 by the operation of the band extending apparatus 1 inthe first example, the base extension signal x_(E)(n) shown in FIG. 6 isgenerated. As shown in FIG. 6, it can be seen that the band of theoriginal signal (i.e. the baseband signal x_(B)(n)) is preferablyextended.

FIG. 7 shows the band limited signal x_(b)(n) obtained from the inputsignal, which is sampled at a sampling frequency of 8 kHz, whose basicfrequency is 437.5 Hz, and in which all the amplitudes of harmonic areequal, by up-sampling the sampling frequency by a factor of 2 and thenextracting a signal component with a band of 2 kHz to 4 kHz.

If the band limited signal x_(b)(n) shown in FIG. 7 is squared by theoperation of the band extending apparatus 1 in the first example, thesignal x_(b) ²(n) shown in FIG. 8 is generated. As shown in FIG. 8, thesignal x_(b) ²(n) has a harmonic relationship with the original signal(i.e. the band limited signal x_(b)(n)), and the signal x_(b) ²(n)includes the double sound component and the sum sound component of theoriginal signal, as well as the direct current component and thedifference sound component of the original signal. However, because theoriginal signal and the signal that does not have a harmonicrelationship with the original signal are not included, the differencesound component and the direct current component can be removed by theHPF 212 having the mild shutoff feature. This results in the generationof the band limited signal x_(b)(n) in which the band (i.e. band of 2kHz to 4 kHz) of the original signal (i.e. the band limited signalx_(b)(n)) is preferably extended to 4 kHz to 8 kHz.

On the other hand, if the band extension process, in which thehigh-frequency signal x_(H)(n) is generated by performing the full-waverectification by the operation of the band extending apparatus in thecomparison example, is performed on the band limited signal x_(b)(n)shown in FIG. 7, not only the double sound component and the sum soundcomponent of the original signal as well as the direct current componentand the difference sound component of the original signal, but also manyunnecessary components which do not have a harmonic relationship withthe original signal or which correspond to the original signal itselfare generated. If it is attempted to extract the double sound componentand the sum sound component, which are originally desired to begenerated, from those unnecessary signal components (in particular, theunnecessary signal components that correspond to the original signalitself), such a HPF (High Pass Filter) that has a large attenuation anda sharp shut off feature is required. However, the HPF having such afeature likely has a large circuit scale (in other words, a large amountof operation or calculation).

According to the band extending apparatus 1 in the first example,however, it is possible to preferably extend the band of the originalsignal by using the HPF 212 having the mild shutoff feature. Moreover,it is also possible to relatively reduce the circuit scale of the bandextending apparatus 1 while preferably extending the band of theoriginal signal.

In addition, since the gain of the high-frequency signal x_(H)(n) isadjusted such that the amplitude level of the high-frequency signalx_(H)(n) matches the amplitude level of the original signal, it ispossible to preferably extend the band of the original signal whilemaintaining the consistency in the signal level with the originalsignal.

(2) Second Example

Next, with reference to FIG. 10, an explanation will be given on asecond example of the band extending apparatus of the present invention.FIG. 10 is a block diagram conceptually showing the basic structure ofthe second example of the band extending apparatus of the presentinvention. Incidentally, the same constituents as those of the bandextending apparatus 1 in the first example described above carry thesame reference numbers, and the detailed explanation thereof will beomitted.

As shown in FIG. 10, in a band extending apparatus 2 in the secondexample, N high-frequency signal generation circuits 21 aremultistage-connected (wherein N is an integer of 2 or more).

In the band extending apparatus 2 in the second example with such astructure, firstly, an up-sampling circuit 112 up-samples the samplingfrequency f_(s) by a factor of 2^(N). Then, a LPF 122 extracts a signalcomponent with a band of 0 to f_(s)/2 (i.e. π/2^(N)), from the inputsignal x(n) whose sampling frequency f_(s) is up-sampled by a factor of2^(N). As a result, the baseband signal x_(B)(n) is extracted.

Then, a BPF 151 extracts a signal component with a band between ½ of theupper-limit frequency of the input signal x(n) and f_(s)/2, from theextracted baseband signal x_(B)(n). As a result, the band limited signalx_(b)(n) is extracted. Then, the high-signal generation circuit 21-(1)generates a high-frequency signal x_(H-(1))(n) from the band limitedsignal x_(b)(n).

The high-frequency signal x_(H-(1))(n) generated on the high-signalgeneration circuit 21-(1) is outputted to a delay circuit 162-(1), andsimultaneously outputted to the high-signal generation circuit 21-(2)which is connected to the next stage of the high-signal generationcircuit 21-(1).

The high-signal generation circuit 21-(2) generates a new high-frequencysignal x_(H-(2))(n) which is higher-frequency than the high-frequencysignal x_(H-(1))(n), from the high-frequency signal x_(H-(1))(n)generated on the high-signal generation circuit 21-(1). Thehigh-frequency signal x_(H-(2))(n) generated on the high-signalgeneration circuit 21-(2) is outputted to a delay circuit 162-(2), andsimultaneously outputted to the high-signal generation circuit 21-(3)which is connected to the next stage of the high-signal generationcircuit 21-(2). Subsequently such an operation is repeated by the numberof the multistage-connected high-signal generation circuits 21.

A delay C(1) added to the high-frequency signal x_(H-(1))(n) on thedelay circuit 162-(1) is a time corresponding to the time required togenerate each of the high-frequency signals x_(H-(2))(n), x_(H-(3))(n),. . . , x_(H-(N))(n) on respective one of the high-signal generationcircuits 21-(2), 21-(3), . . . , 21-(N), which are connected at lowerstages than the high-signal generation circuit 21-(1) corresponding tothe delay circuit 162-(1). In other words, the delay C(1) added to thehigh-frequency signal x_(H-(1))(n) on the delay circuit 162-(1) is thesum of a delay C(2) added on the delay circuit 162-(2) connected at thenext stage of the delay circuit 162-(1) and the time required togenerate the high-frequency signal x_(H-(2))(n) on the high-signalgeneration circuit 21-(2).

That is, a delay C(m) added to the high-frequency signal x_(H-(m))(n) ona delay circuit 162-(m) (wherein 1≦m≦N) is a time corresponding to thetime required to generate each of the high-frequency signalsx_(H-(m+1))(n), x_(H-(m+2))(n), . . . , x_(H-(N))(n) on respective oneof the high-signal generation circuits 21-(m+1), 21-(m+2), . . . ,21-(N), which are connected at lower stages than the high-signalgeneration circuit 21-(m) corresponding to the delay circuit 162-(m). Inother words, the delay C(m) added to the high-frequency signalx_(H-(m))(n) on the delay circuit 162-(m) is the sum of a delay C(m+1)added on the delay circuit 162-(m+1) connected at the next stage of thedelay circuit 162-(m) and the time required to generate thehigh-frequency signal x_(H-(m+1))(n) on the high-signal generationcircuit 21-(m+1).

Moreover, the delay A added to the baseband signal x_(B)(n) on a delaycircuit 132 is the sum of the time required to generate each of thehigh-frequency signals x_(H-(1))(n), x_(H-(2))(n), . . . , x_(H-(N))(n)on respective one of the high-signal generation circuits 21-(1), 21-(2),. . . , 21-(N) and the time required for the process on the BPF 152. Inother words, the delay A added to the baseband signal x_(B)(n) on adelay circuit 132 is the sum of the delay C(1) added on the delaycircuit 162-(1), the time required to generate the high-frequency signalx_(H-(1))(n) on the high-frequency signal generation circuit 21-(1), andthe time required for the process on the BPF 152.

Then, the high-frequency signal x_(H-(N))(n) and the high-frequencysignal x_(H-(N−1))(n) with a delay C(N−1) added are added on an adder142-(N−1), and moreover, to the addition result, the high-frequencysignal x_(H-(N−2))(n) with a delay C(N−2) added is added on an adder 142(N−2). Subsequently, the same operation is repeated by the number of themultistage-connected high-frequency signal generation circuits 21.

According to the band extending apparatus 2 in the second example havingsuch a structure, it is possible to receive the same effects as those ofthe band extending apparatus 1 in the first example described above, andit is possible to extend the input signal so as to have a wider band.Specifically, if the N high-frequency signal generation circuits 21 aremultistage-connected, the band of the input signal x(n) can be extendedby a factor of 2^(N).

(3) Third Example

Next, with reference to FIG. 11 to FIG. 16, an explanation will be givenon a third example of the band extending apparatus of the presentinvention. Incidentally, the same constituents as those of the bandextending apparatus 1 in the first example and the band extendingapparatus 2 in the second example described above carry the samereference numbers, and the detailed explanation thereof will be omitted.

(3-1) Basic Structure

Firstly, with reference to FIG. 11, an explanation will be given on thebasic structure of the third example of the band extending apparatus ofthe present invention. FIG. 11 is a block diagram conceptually showingthe basic structure of the third example of the band extending apparatusof the present invention.

As shown in FIG. 11, a band extending apparatus 3 in the third exampleis provided with: the up-sampling circuit 111; the LPF (Low Pass Filter)121; a blocking circuit 173; a windowing circuit 183; the adder 141; anda high-frequency signal generation circuit 23.

The blocking circuit 173 constitutes one specific example of the“dividing device” of the present invention. The blocking circuit 173performs a blocking process on the baseband signal x_(B)(n) outputtedfrom the LPF 121. More specifically, the blocking circuit 173 dividesthe baseband signal x_(B)(n) into a constant sample number of blocks.Here, in particular, the baseband signal x_(B)(n) is divided such thatthe halves of each block overlaps the respective adjacent blocks. Thatis, the baseband signal x_(B)(n) is divided such that the right half ofeach block is adjacent to the right-adjacent block and that the lefthalf of each block is adjacent to the left-adjacent block. The basebandsignal x_(B)(n) on which the blocking process is performed on theblocking circuit 173 is outputted to the windowing circuit 183 and asquare-root windowing circuit 231 in the high-frequency signalgeneration circuit 23.

The windowing circuit 183 constitutes one specific example of the“windowing device” of the present invention. The windowing circuit 183multiples the baseband signal x_(B)(n) with the blocking processperformed, by a Hanning window. The baseband signal x_(B)(n) multipliedby the Hanning window is outputted to each of a FFT (Fast FourierTransform) circuit 234 in the high-frequency signal generation circuit23 and the adder 141.

The high-frequency signal generation circuit 23 constitutes one specificexample of the “second generating device” of the present invention. Thehigh-frequency signal generation circuit 23 generates the high-frequencysignal x_(H)(n), which is a signal component on the higher-frequencyside than the frequency of the signal components included in the inputsignal x(n). More specifically, the high-frequency signal generationcircuit 23 is provided with: the square-root windowing circuit 231; aFFT circuit 232; a band extraction circuit 233; the FFT circuit 234; anupper-end frequency determination circuit 235; an IFFT (Inverse FastFourier Transform) circuit 236; the square circuit 211; the HPF 212; thegain calculation circuit 214; and the gain adjustment circuit 215.

The square-root windowing circuit constitutes one specific example ofthe “windowing device” of the present invention. The square-rootwindowing circuit multiples the baseband signal x_(B)(n) with theblocking process performed, by the square root of the Hanning window.The baseband signal x_(B)(n) multiplied by the square root of theHanning window is outputted to the FFT circuit 232.

The FFT circuit 232 constitutes one specific example of the “Fouriertransforming device” of the present invention. The FFT circuit 232performs a fast Fourier transform process on the baseband signalx_(B)(n) multiplied by the square root of the Hanning window on thesquare-root windowing circuit 231. The baseband signal on which the fastFourier transform process is performed on the FFT circuit 232(hereinafter the baseband signal on which the fast Fourier transformprocess is performed on the FFT circuit 232, i.e. the output of the FFTcircuit 232, is referred to as a “fast Fourier transform output X(f)) isoutputted to the band extraction circuit 233.

The band extraction circuit 233 constitutes one specific example of the“changing device” of the present invention. The band extraction circuit233 extracts a signal component with a band corresponding to anupper-end frequency f_(U) determined on the upper-end frequencydetermination circuit 235, from the baseband signal with the fastFourier transform process performed, i.e. the fast Fourier transformoutput X(f). The signal component extracted on the band extractioncircuit 233 is outputted to the IFFT circuit 236.

The FFT circuit 234 constitutes one specific example of the “Fouriertransforming device” of the present invention. The FFT circuit 234performs the fast Fourier transform process on the baseband signalx_(B)(n) multiplied by the Hanning window on the windowing circuit 183.The baseband signal on which the fast Fourier transform process isperformed on the FFT circuit 234 is outputted to the upper-end frequencydetermination circuit 235.

The upper-end frequency determination circuit 235 constitutes onespecific example of the “determining device” of the present invention.The upper-end frequency determination circuit 235 determines theupper-end frequency f_(U) of the baseband signal x_(B)(n) on which thefast Fourier transform process is performed on the FFT circuit 234. Theupper-end frequency f_(U) determined on the upper-end frequencydetermination circuit 235 is outputted to the band extraction circuit233.

The IFFT circuit 236 constitutes one specific example of the “inverseFourier transforming device” of the present invention. The IFFT circuit236 performs an inverse Fourier transform process on the signalcomponent extracted on the band extraction circuit 233. As a result, aninverse Fourier transform signal is generated.

The inverse Fourier transform signal is the aforementioned band limitedsignal x_(b)(n), as detailed later. Therefore, using the band limitedsignal x_(b)(n) obtained from the inverse Fourier transform signal, thehigh-frequency signal x_(H)(n) is generated by the operations of thesquare circuit 211, the HPF 212, the gain calculation circuit 214, andthe gain adjustment circuit 215.

(3-2) Operation Principle

Next, with reference to FIG. 12 to FIG. 15, an explanation will be givenon the operation principle of the band extending apparatus 3 in thethird example. FIG. 12 are spectrum views conceptually showing thespectrum of each of the input signal x(n), the baseband signal x_(B)(n),and the signal component extracted by the band extraction circuit 233,related to the operation of the band extending apparatus 3 in the thirdexample. FIG. 13 is an explanatory diagram conceptually showing a blockmultiplied by the Hanning window. FIG. 14 is a spectrum viewconceptually showing an operation of determining the upper-end frequencyf_(U). FIG. 15 are spectrum views conceptually showing the spectrum ofeach of the high-frequency signal x_(H)(n) and the band extension signalx_(E)(n), related to the operation of the band extending apparatus 3 inthe third example.

As shown in FIG. 12( a), it is assumed that the input signal x(n) withthe sampling frequency f_(s) is inputted to the band extending apparatus3.

For the input signal x(n), the up-sampling circuit 111 up-samples thesampling frequency f_(s) by a factor of 2. Then, the LPF 121 extractsthe signal component with the band of 0 to f/2 (i.e. π/2), from theinput signal x(n) whose sampling frequency f_(s) is up-sampled. As aresult, the baseband signal x_(B)(n) shown in FIG. 12( b) is extracted.

After that, the blocking circuit 173 performs the blocking process,which is performed on a time axis, on the baseband signal x_(B)(n).Specifically, the blocking circuit 173 divides the baseband signalx_(B)(n) into a certain sample number of blocks.

Then, the windowing circuit 183 multiplies the baseband signal x_(B)(n)with the blocking process performed, by a Hanning window w(n). Thebaseband signal x_(B)(n) multiplied by the Hanning window w(n) by thewindowing circuit 183 is outputted to the FFT circuit 234. Incidentally,the Hanning window w(n) is a window function which is denoted byw(n)=0.5+0.5 cos(2πn/(N−1)) and in which if each window is½-overlap-added to the adjacent windows, the addition result is 1.

The plurality of blocks multiplied by the Hanning window are shown inFIG. 13. The baseband signal x_(B)(n) on which the blocking process andthe multiplication by the Hanning window are performed, as shown in FIG.13, can receive such an effect that the signal can be regenerated inre-synthesizing each block.

Then, the fast Fourier transform process is performed by the operationof the FFT circuit 234 on the baseband signal x_(B)(n) on which theblocking process and the multiplication by the Hanning window areperformed. That is, the processing area of the baseband signal x_(B)(n)is converted from a time area to a frequency area. As a result, alogarithmic amplitude spectrum of the baseband signal x_(B)(n), on whichthe blocking process and the multiplication by the Hanning window areperformed, is obtained.

Then, the upper-end frequency determination circuit 235 determines theupper-end frequency f_(U), on the basis of the logarithmic amplitudespectrum of the baseband signal x_(B)(n), on which the blocking processand the multiplication by the Hanning window are performed and which isobtained by performing the fast Fourier transform process on the FFTcircuit 234.

In the operation of determining the upper-end frequency, firstly, theamplitude logarithmic spectrum is smoothed by a Savitzky-Golay filter orthe like, to thereby generate a smoothed spectrum as shown in athick-line graph in FIG. 14. Incidentally, the amplitude logarithmicspectrum shown in FIG. 14 shows one example of the amplitude logarithmicspectrum corresponding to the input signal x(n) with a samplingfrequency f_(s) of 8000 Hz.

Then, the graph of the smoothed spectrum is scanned from the frequencyof ½ of the sampling frequency f_(s) of the input signal x(n) to thesmaller frequency side. Then, frequency at a point at which the increaseof spectrum intensity (in other words, amplitude denoted by a decibelvalue) is stopped is determined to be the upper-end frequency f_(U). Forexample, in case of the graph shown in FIG. 14, the smoothed spectrum isscanned from the point of 4000 Hz to the left side of the graph, and thefrequency at the point at which the spectrum intensity is stopped (about3400 Hz in FIG. 14) is determined to be the upper-end frequency f_(U).The determined upper-end frequency f_(U) is outputted to the bandextraction circuit 233.

On the other hand, the baseband signal x_(B)(n) on which the blockingprocess is performed on the blocking circuit 173 is also outputted tothe square-root windowing circuit 231 in the high-frequency signalgeneration circuit 23, in addition to the windowing circuit 183. Thesquare-root windowing circuit 231 multiples the baseband signal x_(B)(n)with the blocking process performed, by the square root of the Hanningwindow w(n) (i.e. (w(n))^(1/2)). The baseband signal x_(B)(n) multipliedby the square root of the Hanning window w(n) by the square-rootwindowing circuit 231 is outputted to the FFT circuit 232.

Incidentally, for the following reason, the square root of the Hanningwindow w(n) is multiplied on the windowing circuit 231. As detailedlater, in the third example, the high-frequency signal x_(H)(n) isgenerated by squaring the band limited signal x_(b)(n), which isobtained from the baseband signal x_(B)(n) with the blocking processperformed. Thus, considering that the band limited signal x_(b)(n) ismultiplied twice by the Hanning window w(n), which is expected to causean impact, the high-frequency signal x_(H)(n) is multiplied by thesquare of the Hanning window w(n). Therefore, in order to realize thesituation that the high-frequency signal x_(H)(n) is multiplied by theHanning window w(n) when the band limited signal x_(b)(n) is squared,the baseband signal x_(B)(n) is multiplied by the square root of theHanning window w(n).

Then, the fast Fourier transform process is performed by the operationof the FFT circuit 232 on the baseband signal x_(B)(n) on which theblocking process and the multiplication by the square root of theHanning window are performed. The fast Fourier transform output X(f) onwhich the fast Fourier transform process is performed on the FFT circuit232 is outputted to the band extraction circuit 233.

Then, a signal component with a band of f_(U)/2 to f_(s)/2 as shown inFIG. 12( c) is extracted from the fast Fourier transform output X(f), bythe operation of the band extraction circuit 233.

Specifically, of the fast Fourier transform output X(f), the spectrumintensity of the signal components with bands of f_(U)/2 to f_(s)/2 and−f_(s)/2 to −f_(U)/2 is maintained. On the other hand, of the fastFourier transform output X(f), the spectrum intensity of the signalcomponent other than the signal components with bands of f_(U)/2 tof_(s)/2 and −f_(s)/2 to −f_(U)/2 is zero-valued. That is, if the fastFourier transform output X(f) in which the spectrum intensity is changedis denoted by Z(f), Z(f)=X(f), for f_(U)/2≦|f|≦f_(s)/2; =0, for|f|<f_(U)/2 or f_(s)/2<|f|.

Then, the IFFT circuit 236 performs the inverse Fourier transformprocess on the fast Fourier transform output Z(f) in which the spectrumintensity is changed. As a result, the band limited signal x_(b)(n) isgenerated.

Thus, subsequently, as in the band extending apparatus 1 in the firstexample described above, the band limited signal x_(b)(n) is squared,and the signal component on the higher-frequency side is extracted fromthe squared band limited signal x_(b) ²(n), to thereby generate thehigh-frequency signal x_(H)(n) as shown in FIG. 15( a). Moreover, evenin the third example, as in the first example, such a process isperformed that corrects the amplitude level of the high-frequency signalx_(H)(n) generated on the multiplier 213, to the original amplitudelevel order. Then, the high-frequency signal x_(H)(n) with that processperformed is added to the baseband signal x_(B)(n) on the adder 141. Asa result, as shown in FIG. 15( b), the band extension signal x_(E)(n) isgenerated.

Incidentally, in the third example, since the baseband signal x_(b)(n)is blocked by the operation of the blocking circuit 173, the bandextension signal x_(E)(n) is ½-overlap-added to the adjacent blocks onthe adder 141.

Now, with reference to FIG. 16, an explanation will be given on thehigh-frequency signal x_(H)(n) generated by the band extending apparatus3 in the third example. FIG. 16 is a spectrum view showing the signalx_(b) ²(n) obtained by squaring the band limited signal x_(b)(n) shownin FIG. 7.

The band limited signal x_(b)(n) obtained from the input signal which issampled at a sampling frequency of 8 kHz, whose basic frequency is 437.5Hz, and in which all the amplitudes of high harmonic signal are equal,by up-sampling the sampling frequency by a factor of 2 and thenextracting a signal component with a band of 2 kHz to 4 kHz (i.e. theband limited signal x_(b)(n) shown in FIG. 7 described above) is squaredby the operation of the band extending apparatus 3 in the third example,by which the signal x_(b) ²(n) shown in FIG. 16 is generated. As shownin FIG. 16, the signal x_(b) ²(n) has a harmonic relationship with theoriginal signal (i.e. the band limited signal x_(b)(n)), and the signalx_(b) ²(n) includes the double sound component and the sum soundcomponent of the original signal, as well as the direct currentcomponent and the difference sound component of the original signal.However, because the original signal and the signal that does not have aharmonic relationship with the original signal are not included, thedifference sound component and the direct current component can beremoved by the HPF 212 having the mild shutoff feature. This results inthe generation of the band limited signal x_(b)(n) in which the band(i.e. band of 2 kHz to 4 kHz) of the original signal (i.e. the bandlimited signal x_(b)(n)) is preferably extended to 4 kHz to 8 kHz.

As described above, according to the band extending apparatus 3 in thethird example, it is possible to receive the same effects as those ofthe band extending apparatus 1 in the first example described above.

In addition, in the third example, the logarithmic spectrum of theoriginal signal (i.e. the band limited signal x_(b)(n)) is smoothed todetermine the upper-end frequency f_(U), and then the signal componentwith a band that is a basis for generating the high-frequency signalx_(H)(n) is extracted on the basis of the upper-end frequency f_(U).Thus, in accordance with the upper-end frequency f_(U) of the originalsignal, the high-frequency signal x_(H)(n) can be generatedappropriately. That is, in the first example, the signal component witha band that is a basis for generating the high-frequency signal x_(H)(n)is extracted fixedly from the BPF 151; however in the third example, itis possible to extract the signal component with a preferable bandcorresponding to the original signal, as the signal component with aband that is a basis for generating the high-frequency signal x_(H)(n).By this, it is possible to preferably generate the high-frequency signalx_(H)(n) suitable for the original signal (e.g. so as to be added to theoriginal signal continuously or smoothly).

(4) Fourth Example

Next, with reference to FIG. 17, an explanation will be given on afourth example of the band extending apparatus of the present invention.FIG. 17 is a block diagram conceptually showing the basic structure ofthe fourth example of the band extending apparatus of the presentinvention. Incidentally, the same constituents as those of the bandextending apparatus 1 in the first example, the band extending apparatus2 in the second example, or the band extending apparatus 3 in the thirdexample described above carry the same reference numbers, and thedetailed explanation thereof will be omitted.

As shown in FIG. 17, in a band extending apparatus 4 in the fourthexample, the FFT circuit 234 and the windowing circuit 183 areeliminated, as compared to the band extending apparatus 3 in the thirdexample. In the band extending apparatus 4 in the fourth example, theprocess performed on the FFT circuit 234 is performed on the FFT circuit232, and the process performed on the windowing circuit 183 is performedon the square-root windowing circuit 231.

Specifically, the square-root windowing circuit 231 multiplies thebaseband signal x_(B)(n) with the blocking process performed, by thesquare root of the Hanning window w(n). Then, the fast Fourier transformprocess is performed by the operation of the FFT circuit 232 on thebaseband signal x_(B)(n) on which the blocking process and themultiplication by the square root of the Hanning window are performed.That is, the processing area of the baseband signal x_(B)(n) isconverted from the time area to the frequency area. As a result, thelogarithmic amplitude spectrum (i.e. the fast Fourier transform outputX(f)) is generated. The generated logarithmic amplitude spectrum isoutputted to each of the upper-end frequency determination circuit 235and the band extraction circuit 233. Then, the high-frequency signalx_(H)(n) is generated by the same operation as that of the bandextending apparatus 3 in the third example described above.

As described above, according to the band extending apparatus 4 in thefourth example, it is possible to generate the fast Fourier transformoutput X(f) used to determine the upper-end frequency f_(U) and the fastFourier transform output X(f) for extracting the signal component withthe band that is a basis for generating the high-frequency signalx_(H)(n), by using the same square-root windowing circuit 231 and theFFT circuit 232. In other words, in order to generate the fast Fouriertransform output X(f) used to determine the upper-end frequency f_(U)and the fast Fourier transform output X(f) for extracting the signalcomponent with the band that is a basis for generating thehigh-frequency signal x_(H)(n), it is unnecessary to provide thewindowing circuit and the FFT circuit separately for the two objectives.Thus, according to the band extending apparatus 4 in the fourth example,it is possible to appropriately receive the same effects as thosereceived by the band extending apparatus 3 in the third example, and itis also possible to simplify the circuit structure, as compared to theband extending apparatus 3 in the third example.

(5) Fifth Example

Next, with reference to FIG. 18, an explanation will be given on a fifthexample of the band extending apparatus of the present invention. FIG.18 is a block diagram conceptually showing the basic structure of thefifth example of the band extending apparatus of the present invention.Incidentally, the same constituents as those of the band extendingapparatus 1 in the first example, the band extending apparatus 2 in thesecond example, the band extending apparatus 3 in the third example, orthe band extending apparatus 4 in the fourth example described abovecarry the same reference numbers, and the detailed explanation thereofwill be omitted.

As shown in FIG. 18, in a band extending apparatus 5 in the fifthexample, N high-frequency signal generation circuits 23 aremultistage-connected (wherein N is an integer of 2 or more).

In the band extending apparatus 5 in the fifth example with such astructure, firstly, the up-sampling circuit 112 up-samples the samplingfrequency f_(s) by a factor of 2N. Then, the LPF 122 extracts the signalcomponent with a band of 0 to f_(s)/2 (i.e. π/2^(N)), from the inputsignal x(n) whose sampling frequency f, is up-sampled by a factor of2^(N). As a result, the baseband signal x_(B)(n) is extracted.

Then, each of the baseband signal x_(B)(n) on which the blocking processis performed on the blocking circuit 173 and the baseband signalx_(B)(n) which is multiplied by the Hanning window w(n) on the windowingcircuit 183 is outputted to the high-frequency signal generation circuit23-(1).

Then, on the high-frequency signal generation circuit 23-(1), theupper-end frequency f_(U) is determined on the basis of the basebandsignal x_(B)(n) multiplied by the Hanning window w(n). Moreover, by theband extraction circuit 233 in the high-frequency signal generationcircuit 23-(1), the signal component with a band between ½ of theupper-end frequency of the input signal x(n) and the f_(s)/2 isextracted from the fast Fourier transform output X(f) generated by thatthe FFT circuit 232 in the high-frequency signal generation circuit23-(1) performs the Fourier transform process on the baseband signalx_(B)(n). Then, the inverse Fourier transform process is performed onZ(f) obtained by doubling the spectrum intensity of the signal componentextracted by the band extraction circuit 233 and zeroing the spectrumintensity of the signal component other than the signal componentextracted by the band extraction circuit 233, to thereby generate ahigh-frequency signal x_(H-(1))(n).

The high-frequency signal x_(H-(1))(n) generated on the high-frequencysignal generation circuit 23-(1) is outputted to an adder 142-(1) andsimultaneously outputted to the high-frequency signal generation circuit23-(2), which is connected to the next stage of the high-frequencysignal generation circuit 23-(1).

The high-signal generation circuit 23-(2) generates a new high-frequencysignal x_(H-(2))(n) which is higher-frequency than the high-frequencysignal x_(H-(1))(n), from the high-frequency signal x_(H-(1))(n)generated on the high-signal generation circuit 23-(1). Thehigh-frequency signal x_(H-(2))(n) generated on the high-signalgeneration circuit 23-(2) is outputted to an adder circuit 142-(2), andsimultaneously outputted to the high-signal generation circuit 23-(3)which is connected to the next stage of the high-signal generationcircuit 23-(2). Subsequently such an operation is repeated by the numberof the multistage-connected high-signal generation circuits 23.

Then, a high-frequency signal x_(H-(N))(n) generated on the high-signalgeneration circuit 23-(N) and a high-frequency signal x_(H-(N−1))(n)generated on the high-signal generation circuit 23-(N−1) are added on anadder 142-(N−1), and moreover, to the addition result, a high-frequencysignal x_(H-(N−2))(n) generated on high-signal generation circuit23-(N−2) is added on an adder 142-(N−2). Subsequently, the sameoperation is repeated by the number of the multistage-connectedhigh-signal generation circuits 23.

According to the band extending apparatus 5 in the fifth example withsuch a structure, it is possible to receive the same effects as those ofthe band extending apparatus 3 in the third example described above, andit is also possible to extend the input signal x(n) so as to have awider band. Specifically, if the N high-frequency signal generationcircuits 23 are multistage-connected, the band of the input signal x(n)can be extended by a factor of 2^(N).

(6) Example of Application to Actual Product

Next, with reference to FIG. 19, an explanation will be given on thecase where the band extending apparatus 1 in the first example, the bandextending apparatus 2 in the second example, the band extendingapparatus 3 in the third example, the band extending apparatus 4 in thefourth example, or the band extending apparatus 5 in the fifth exampledescribed above is applied to various acoustic equipment. FIG. 19 areblock diagrams conceptually showing the structure when the bandextending apparatus is applied to various products.

FIG. 19( a) shows an example in which the band extending apparatus 1 inthe first example, the band extending apparatus 2 in the second example,the band extending apparatus 3 in the third example, the band extendingapparatus 4 in the fourth example, or the band extending apparatus 5 inthe fifth example described above is applied to a CD player, a DVDplayer, or the like. In the CD player, the DVD player, or the like, anaudio signal in a linear PCM format is treated as the input signal x(n).The audio signal with the band extended on the band extending apparatus1 is converted to an analog signal on a D/A converter and then outputtedto output equipment such as a speaker.

FIG. 19( b) shows an example in which the band extending apparatus 1 inthe first example, the band extending apparatus 2 in the second example,the band extending apparatus 3 in the third example, the band extendingapparatus 4 in the fourth example, or the band extending apparatus 5 inthe fifth example described above is applied to a MD player, a MD3player, or the like. In the MD player, the MD3 player, or the like, anaudio signal on which a decoding process is performed on a compressionaudio decoder (e.g. a MP3 decoder, an ATRAC3 decoder, or the like) istreated as the input signal x(n). The audio signal with the bandextended on the band extending apparatus 1 is converted to an analogsignal on a D/A converter and then outputted to output equipment such asa speaker.

FIG. 19( c) shows an example in which the band extending apparatus 1 inthe first example, the band extending apparatus 2 in the second example,the band extending apparatus 3 in the third example, the band extendingapparatus 4 in the fourth example, or the band extending apparatus 5 inthe fifth example described above is applied to a mobile phone or thelike. In the mobile phone or the like, in general, a compression-encodedaudio signal is transmitted and received. Thus, in the mobile phone orthe like, an audio signal on which the decoding process is performed ona decoder is treated as the input signal x(n). The audio signal with theband extended on the band extending apparatus 1 is converted to ananalog signal on a D/A converter and then outputted to output equipmentsuch as a speaker.

FIG. 19( d) shows an example in which the band extending apparatus 1 inthe first example, the band extending apparatus 2 in the second example,the band extending apparatus 3 in the third example, the band extendingapparatus 4 in the fourth example, or the band extending apparatus 5 inthe fifth example described above is applied to a FM radio or the like.In the FM radio or the like, a FM signal which is extracted by the LPFwith a cutoff frequency of about 15 kHz and which is converted to adigital signal by an A/D converter (i.e. an audio signal included in theFM signal) is treated as the input signal x(n). The audio signal withthe band extended on the band extending apparatus 1 is converted to ananalog signal on a D/A converter and then outputted to output equipmentsuch as a speaker.

FIG. 19( e) shows an example in which the band extending apparatus 1 inthe first example, the band extending apparatus 2 in the second example,the band extending apparatus 3 in the third example, the band extendingapparatus 4 in the fourth example, or the band extending apparatus 5 inthe fifth example described above is applied to an AM radio or the like.In the AM radio or the like, an AM signal which is extracted by the LPFwith a cutoff frequency of about 7.5 kHz and which is converted to adigital signal by an A/D converter (i.e. an audio signal included in theAM signal) is treated as the input signal x(n). The audio signal withthe band extended on the band extending apparatus 1 is converted to ananalog signal on the D/A converter and then outputted to outputequipment such as a speaker.

The present invention is not limited to the aforementioned examples, butvarious changes may be made, if desired, without departing from theessence or spirit of the invention which can be read from the claims andthe entire specification. A band extending apparatus and method, all ofwhich involve such changes, are also intended to be within the technicalscope of the present invention.

1-10. (canceled)
 11. A band extending apparatus comprising: a first generating device for generating a baseband signal by up-sampling an input signal and then transmitting it through a low-pass filter; a second generating device for generating a high-frequency signal, which is a signal component corresponding to the input signal and which is a signal component on a higher-frequency side than the input signal, by extracting a signal component on a higher-frequency side of a signal which is obtained by squaring a band limited signal, the band limited signal is a signal component with a predetermined band of the baseband signal; and a third generating device for generating an output signal by adding the high-frequency signal to the baseband signal, said second generating device further comprises: a Fourier transforming device for generating a Fourier transform signal by performing a Fourier transform process on the baseband signal; a determining device for determining a frequency at which a signal level of the Fourier transform signal is suddenly dropped, as an upper-end frequency; a changing device for changing a level of the Fourier transform signal so as to maintain a level of a signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal, and to zero a level of a signal component other than the signal component with the band defined in accordance with the upper-end frequency, of the Fourier transform signal; and an inverse Fourier transforming device for generating an inverse Fourier transform signal by performing an inverse Fourier transform process on the Fourier transform signal in which the level is changed by the changing device, and said second generating device generates the high-frequency signal, with using the inverse Fourier transform signal as the band limited signal.
 12. The band extending apparatus according to claim 11, wherein said second generating device generates the high-frequency signal by adjusting a gain of the high-frequency signal in accordance with an absolute value of the band limited signal.
 13. The band extending apparatus according to claim 11, further comprising a delaying device for adding a delay corresponding to a time required for the generation of the high-frequency signal by said second generating device, to the baseband signal, said third generating device adding the high-frequency signal to the baseband signal to which the delay corresponding to the time required for the generation of the high-frequency signal by said second generating device is added.
 14. The band extending apparatus according to claim 11, wherein the predetermined band is a band ranged between ½ of an upper-end frequency of the input signal and ½ of a sampling frequency of the input signal before being up-sampled.
 15. The band extending apparatus according to claim 11, wherein the changing device changes the level of the Fourier transform signal so as to maintain a level of a signal component with a band ranged between ½ of the upper-end frequency and ½ of a sampling frequency of the input signal before being up-sampled, of the Fourier transform signal, and to zero a level of a signal component other than the signal component with the band ranged between ½ of the upper-end frequency and ½ of the sampling frequency of the input signal before being up-sampled, of the Fourier transform signal.
 16. The band extending apparatus according to claim 11, wherein said band extending apparatus further comprises: a dividing device for dividing the baseband signal into a plurality of block in which one portion of each of the plurality of blocks overlaps adjacent blocks; and a first windowing device for performing a windowing process using a Hanning window, on the baseband signal divided into the plurality of blocks, said second generating device further comprises a second windowing device for performing a windowing process using a square root of a Hanning window, on the baseband signal divided into the plurality of blocks, said Fourier transforming device performs the Fourier transform process on each of the baseband signal on which the windowing process using the Hanning window is performed and the baseband signal on which the windowing process using the square root of the Hanning window is performed, said determining device determines the frequency at which the signal level of the Fourier transform signal, generated by performing the Fourier transform process on the baseband signal on which the windowing process using the Hanning window is performed, is suddenly dropped, as the upper-end frequency, and said changing device changes the level of the Fourier transform signal so as to maintain a level of a signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal generated by performing the Fourier transform process on the baseband signal on which the windowing process using the square root of the Hanning window is performed, and to zero a level of a signal component other than the signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal generated by performing the Fourier transform process on the baseband signal on which the windowing process using the square root of the Hanning window is performed.
 17. The band extending apparatus according to claim 11, wherein said band extending apparatus further comprises a dividing device for dividing the baseband signal into a plurality of block in which one portion of each of the plurality of blocks overlaps adjacent blocks, said second generating device further comprises a windowing device for performing a windowing process using a square root of a Hanning window, on the baseband signal divided into the plurality of blocks, said Fourier transforming device performs the Fourier transform process on each of the baseband signal on which the windowing process using the square root of the Hanning window is performed, said determining device determines the frequency at which the signal level of the Fourier transform signal, generated by performing the Fourier transform process on the baseband signal on which the windowing process using the square root of the Hanning window is performed, is suddenly dropped, as the upper-end frequency, and said changing device changes the level of the Fourier transform signal so as to maintain a level of a signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal generated by performing the Fourier transform process on the baseband signal on which the windowing process using the square root of the Hanning window is performed, and to zero a level of a signal component other than the signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal generated by performing the Fourier transform process on the baseband signal on which the windowing process using the square root of the Hanning window is performed.
 18. The band extending apparatus according to claim 11, wherein said band extending apparatus comprises a plurality of second generating devices, and one second generating device of the plurality of second generating devices generates a new high-frequency signal by extracting a signal component on a higher-frequency side of a signal obtained by squaring the high-frequency signal, which is generated by at least one of the second generating devices other than the one second generating device.
 19. A band extending method comprising: a first generating process of generating a baseband signal by up-sampling an input signal and then transmitting it through a low-pass filter; a second generating process of generating a high-frequency signal, which is a signal component corresponding to the input signal and which is a signal component on a higher-frequency side than the input signal, on the basis of a signal component on a higher-frequency side of a signal which is obtained by squaring a band limited signal, the band limited signal is a signal component with a predetermined band of the baseband signal; and a third generating process of generating an output signal by adding the high-frequency signal to the baseband signal, said second generating process further comprises: a Fourier transforming process of generating a Fourier transform signal by performing a Fourier transform process on the baseband signal; a determining process of determining a frequency at which a signal level of the Fourier transform signal is suddenly dropped, as an upper-end frequency; a changing process of changing a level of the Fourier transform signal so as to maintain a level of a signal component with a band defined in accordance with the upper-end frequency, of the Fourier transform signal, and to zero a level of a signal component other than the signal component with the band defined in accordance with the upper-end frequency, of the Fourier transform signal; and an inverse Fourier transforming process of generating an inverse Fourier transform signal by performing an inverse Fourier transform process on the Fourier transform signal in which the level is changed by the changing process, and said second generating process generates the high-frequency signal, with using the inverse Fourier transform signal as the band limited signal.
 20. A band extending apparatus comprising: a first generating device for generating a baseband signal by up-sampling an input signal and then transmitting it through a low-pass filter; a first windowing device for performing a windowing process using a Hanning window, on the generated baseband signal; a second windowing device for performing a windowing process using a square root of a Hanning window, on the generated baseband signal; a second generating device for generating a high-frequency signal, which is a signal component corresponding to the input signal and which is a signal component on a higher-frequency side than the input signal, by extracting a signal component on a higher-frequency side of a signal obtained by squaring a band limited signal, the band limited signal is a signal component with a predetermined band of the baseband signal with the windowing process performed; and a third generating device for generating an output signal by adding the high-frequency signal to the baseband signal with the windowing process performed by said first windowing device.
 21. A band extending method comprising: a first generating process of generating a baseband signal by up-sampling an input signal and then transmitting it through a low-pass filter; a first windowing process of performing a windowing process using a Hanning window, on the generated baseband signal; a second windowing process of performing a windowing process using a square root of a Hanning window, on the generated baseband signal; a second generating process of generating a high-frequency signal, which is a signal component corresponding to the input signal and which is a signal component on a higher-frequency side than the input signal, on the basis of a signal component on a higher-frequency side of a signal obtained by squaring a band limited signal, the band limited signal is a signal component with a predetermined band of the baseband signal with the windowing process performed; and a third generating process of generating an output signal by adding the high-frequency signal to the baseband signal with the windowing process performed by said first windowing process. 